POST UTME AAUA 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A company has two factories, A and B, producing a total of 1000 units per day. Factory A produces 60% of the total units, while factory B produces the remaining 40%. If the profit per unit from factory A is ₦50 and from factory B is ₦30, what is the total profit per day?
A. ₦3500
B. ₦4000
C. ₦4500
D. ₦5000
Question 2
A curve is defined by the equation y = x^2 + 2x + 1. Find the area under the curve between x = 0 and x = 2.
A. 6
B. 7
C. 8
D. 9
Question 3
Find the area under the curve \( y = \sin x \) from \( x = 0 \) to \( x = \frac{pi}{2} \) u\sing integration.
A. \( \frac{pi}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{2} \)
D. \( \frac{pi}{4} \)
Question 4
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected student will score above 80?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6745
Question 5
Let \( vec{a} = egin{bmatrix} 1 \ 2 \ 3 \end{bmatrix} \) and \( vec{b} = egin{bmatrix} 4 \ 5 \ 6 \end{bmatrix} \). Find the cross product \( vec{a} \times vec{b} \).
A. \( egin{bmatrix} 3 \ 6 \ 9 \end{bmatrix} \)
B. \( egin{bmatrix} 6 \ 9 \ 12 \end{bmatrix} \)
C. \( egin{bmatrix} 9 \ 12 \ 15 \end{bmatrix} \)
D. \( egin{bmatrix} 12 \ 15 \ 18 \end{bmatrix} \)
Question 6
Find the area of the region bounded by the curves \( y = x^2 \) and \( y = 2x \).
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{4}{3}
D. \frac{5}{3}
Question 7
A random sample of 16 students from a population of 50 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. Calculate the s\tandard error of the mean.
A. 2.5 cm
B. 3.5 cm
C. 4.5 cm
D. 5.5 cm
Question 8
In a 3x3 matrix, if the determinant is 12, and one of the elements is 4, what is the sum of the other two elements in the same row?
A. 5
B. 6
C. 7
D. 8
Question 9
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{16}{3} \)
B. ( 8 )
C. ( 16 )
D. ( 32 )
Question 10
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{6} \)
Question 11
A quadratic equation is defined by the equation x^2 + 4x + 4 = 0. Find the sum of the roots.
A. 0
B. -2
C. -4
D. -6
Question 12
Find the volume of the solid formed by revolving the region bounded by the curve y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 13
Let ( f(x) = \frac{1}{x^2 + 1} ). Find the value of \( int_{0}^{\frac{pi}{4}} f\( x \ \) , dx ).
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{1}{3}
D. \frac{1}{5}
Question 14
Solve the inequality \( \frac{x - 2}{x + 1} > 0 \) u\sing interval notation.
A. \( -infty, -1 \ \) cup (2, infty) )
B. \( -infty, -1 \ \) cup (1, 2) )
C. \( -infty, -1 \ \) cup (2, infty) )
D. \( -infty, -1 \ \) cup (1, 2) )
Question 15
Solve for x in the equation \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. -1
D. 1

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